1. Field of the Invention
The present invention generally relates to the area of data communication, and more particularly to a transmission system using a code designed to provide reliable broadcast information to multiple receivers over different channels.
2. Brief Description of the Prior Art
In a data communication system where the transmitter cannot be specialized to the impulse response of any particular channel or the transmitter does not have a reliable feedback link over which to learn the signal characteristics of the channels, system performance or capacity may be severely impaired. An example of such a situation where the transmitter cannot be specialized to the channels is when information is broadcasted to multiple users over different channels such as with digital audio broadcast system (DAB) or High Definition Television System (HDTV).
In these cases, in order to obtain good performance, orthogonal frequency division multiplexing (OFDM) is used.
Orthogonal frequency division multiplexing is a form of multicarrier modulation and is an alternative to equalized single carrier modulation. Multicarrier modulation is especially attractive in environments where severe intersymbol interference (ISI) makes equalization difficult. Terrestrial wireless broadcast from multiple towers is an example of a severe ISI environment where multicarrier modulation is attractive. Hikmet Sari, Georges Karam, and Isabelle Jeanclaude, Transmission Techniques for Digital Terrestrial TV Broadcasting, IEEE Communications Magazine, 33(2):100-109, February 1995.
A well known form of multicarrier modulation which uses discrete Fourier transformation (DFT) is shown in FIG. 1. Signal values x.sub.k 10, which are produced by a coded modulation scheme, are processed by inverse discrete Fourier transformation (IDFT) 12 and transmitted through a transmission medium (or channel) 14. The information is then received and processed by discrete Fourier transformation (DFT) 16 to produce the received signal points y.sub.k 18 which are then processed by a decoder. When bits and power are distributed evenly across the subcarriers by the transmitter, such a method is referred to as orthogonal frequency division multiplexing (OFDM).
The motivation for using OFDM is illustrated in FIG. 2. A single additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) is converted to a number of parallel AWGN sub-channels that have no ISI, k=1 . . . N. Each sub-channel consists only of a scale factor, a.sub.k, and AWGN, n.sub.k. The complex scale factors, a.sub.k, are exactly the values of the DFT of the channel impulse response. For an AWGN channel with ISI, the noise has a flat spectrum so that E[n.sub.k.sup.2 ]=E[n.sup.2 ] for all k. A cyclic prefix (guard interval) approximately the length of the channel impulse response is inserted between each DFT block in order for the transformation to parallel channels to be exact.
Note that the equalization problem has not been solved by the use of multiple carriers. Rather, the equalization problem has been transformed to a problem of coding over parallel channels with unequal signal-to-noise ratios (SNRs). When the SNR of each subcarrier is known, the coding problem can be resolved by placing an appropriate number of bits on each subcarrier. However, in a broadcast situation or in a system without feedback from the receiver, the subcarriers' SNRs are not known. In this type of situation, coding and interleaving must allow the high SNR subcarriers to compensate for the low SNR subcarriers regardless of which subcarriers have high or low SNR.
To achieve the highest possible performance, a system's performance should be compared with the best performance obtainable as predicted by the relevant theory. For example, the performance for a given code on a transmission system on AWGN channels is typically quantified by the difference between the required SNR for a given code to achieve a desired error rate and the required SNR of an ideal code from information theory for error free transmission.
When a given code must operate on a variety of channels with a variety of channel characteristics, performance on each channel should be compared with theoretical performance using a measure that is consistent across the channels. The channel having performance farthest from the theoretical performance limit can then be identified as demonstrating a weakness in the code. A good code would result in approximately the same BER for all the channels having the same capacity.
To effectively evaluate the performance of codes over a variety of channels, let alone design codes that will perform well, the theoretical performance limits need to be established.
For any specified set of transmitter powers {E[x.sub.k.sup.2 ]}, the mutual information (MI) of a channel described by FIG. 2 is given by ##EQU1## The mutual information equals the capacity of the channel if the values of {E[x.sub.k.sup.2 ]} are chosen to have the optimal water-pouring distribution. However, in an OFDM system, such optimal distribution cannot be used because channel characteristic is not known at the transmitter. The term mutual information is used here to describe the maximum amount of information that can be transmitted across the channel given a fixed transmit power spectrum.
Shannon's fundamental coding theorem ensures that for each AWGN channel with ISI there is a code that will reliably transmit at a rate equal to the mutual information corresponding to the chosen input power distribution. More crucial for the broadcast situation is Root and Varaiya's 1968 result shown in their article, Capacity of Classes of Gaussian Channels (Siam Journal of Applied Math 16(6):1350-1393, November 1968), stating that for any given data rate and fixed transmitter power distribution there exists a "universal" code that will reliably transmit over all channels that have mutual informations at or above the attempted rate.
Such a code is ideal for point-to-point transmission over fading channels or broadcast over a variety of channels. Codes with a practical level of complexity combined with OFDM and periodic interleaving which approximate this universal behavior are disclosed by the present invention. In subsequent paragraphs, metrics are presented to identify the degree to which a code is considered to be "universal". The problem with the transmission systems designed under the prior art is that they do not provide consistent performance over a variety of channels which all have the same capacity given a fixed transmitter power spectrum. Even though consistent performance is possible in theory, a transmission system providing such performance has not been forthcoming. The present invention discloses transmission systems using codes that provide consistent and reliable performance over a wide variety of channels having the same capacity.
Two prior art metrics are introduced here to provide the basis for understanding the novel metrics of the present invention. Divsalar and Simon proposed in their article, The Design of Trellis Coded for Fading Channels: Performance Criteria (IEEE Transactions on Communications, 36(9):1004-1012, September 1988), two metrics, effective code length (ECL) and product distance, as important metrics in the design of trellis codes for fading channels. They also analytically demonstrated the value as indicators of code performance on Rician channels. These metrics were discussed by Sundberg and Seshadri in their article, Coded Modulation for Fading Channels: An Overview (European Transactions on Telecommunications, 4(3):309-323, May-June 1993), as well as in many other papers. Rate .sup.n-1 /.sub.n trellis codes have been designed according to these metrics by Du and Vucetic and are published in their articles, J. Du and B. Vucetic, New M-PSK Trellis Codes for Fading Channels (Electronics Letters, 26(16):1267-1269, August 1990), J. Du and B. Vucetic, New 16-QAM Trellis Codes for Fading Channels (Electronics Letters, 27(12):1009-1010, June 1991), J. Du, Y. Kamio, H. Sasaoka, and B. Vucetic, New 32-QAM Trellis Codes for Fading Channels (Electronics Letters, 29(20):1745-1746, September 1993).
The ECL of a code is defined to be the minimum number of symbol errors required for an error event to occur. The product distance is defined as the minimum product of the squared Euclidean distances associated with an error event having a fixed (usually minimum) ECL.